The Problem of Symmetrical Threats

Tim Campbell is a PhD student at Rutgers University who will soon be starting a postdoc at the Institute for Futures Studies in Stockholm. At the recently concluded Rocky Mountain Ethics Congress, his third, Campbell gave a talk called “The Problem of Symmetrical Threats”. In it, he identified a potentially serious problem for the standard account of self-defense. What follows is a short version of that paper, though it is still not short for a typical blog post. What’s Wrong? intends to experiment with postings of a variety of lengths, welcomes submissions from op-ed to journal article length, and is grateful to Campbell for providing this version to share with its readers.

The Problem of Symmetrical Threats

1. Introduction

Most theories of self-defense recognize at least one non-consequentialist justification for killing a person, which appeals to the claim that the person to be killed has acted in such a way that killing her wouldn’t wrong her, even if she hasn’t consented to be killed. Following Jeff McMahan, I shall say that such a person is liable to be killed.[1] According to the most popular account, one becomes liable to be killed by threatening impermissibly to kill or seriously injure another. This makes it permissible to threaten to kill one, provided that threatening to kill one is necessary for stopping one’s threat and proportionate, i.e., it doesn’t violate anyone else’s rights or produce any bad effect that outweighs the good achieved by stopping one’s threat. On the other hand, if one isn’t liable to be killed, then killing one is impermissible unless there is some overriding justification for killing one. Call this the Standard View of the ethics of defensive killing.[2]

The Standard View has two parts. The first part specifies when one is liable to be killed. I call this

Liability Condition: x is liable to be killed for threatening to kill or seriously injure y iff (i) the act by which x threatens y is impermissible and (ii) x meets any subjective criteria that are necessary for x’s being liable to be killed.

The second part specifies when it is permissible to threaten to kill one who is liable to be killed. I call this

Defensive Condition: If x threatens to kill y and x doesn’t have a non-liability-based permission to threaten to kill y, then the act by which x threatens to kill y is permissible iff (iii) y is liable to defensive killing, and (iv) x’s act is both necessary and proportionate.

I will argue that the Standard View is threatened by the following kind of case:

Symmetry Case 1. Smith maliciously intends to kill his archrival, Jones, by shooting him with a sniper rifle. Jones maliciously intends to kill Smith in precisely the same manner. As Smith peers through the scope of his rifle, he sees Jones looking back at him through the scope of a similar rifle. Still acting with malicious intent, and now realizing that his life is under threat, each rushes to kill the other before the other can kill him. They fire simultaneously.[3]

I stipulate the following:

1. Symmetrical Self-Defense Assumption: Smith and Jones are what I call symmetrical self-defenders or ‘defenders’ for short. This means that the following assertions are true of them:

a. Each threatens to kill the other.

b. With respect to each, the act by which he threatens the other—in this case pulling the trigger—is initiated no earlier than the act by which the other threatens him.

c. Each will kill the other if the other does not kill him.

d. Each threatens no one but the other.

e. All other morally relevant factors, such as the causal mechanisms through which their threats are carried out, their reasons for threatening each other, and the intentions, motives, etc., with which they act are the same in every respect that is relevant for determining the permissibility of their acts as well as the harm to which they are liable.

2. Necessity Assumption: With respect to each defender, the act by which he threatens to kill the other is necessary. (This follows straightaway from 1c.)

3. Proportionality Assumption: With respect to each defender, the act by which he threatens to kill the other is proportionate if the other is liable to be killed.

4. Subjective Assumption: Each satisfies any subjective criteria that are necessary for his being liable to be killed.

In addition to stipulations 1—4, the following four claims seem very plausible:

5. No Other Permission: Neither defender has a non-liability-based permission to kill anyone—that is, a permission that appeals to considerations other than liability.

6. No Deontic Gap: With respect to each defender, his act is either permissible or impermissible.

7. Deontic Monoletheism: An act is permissible only if it isn’t impermissible.

8 Symmetry: If A and B are symmetrical self-defenders (i.e. if 1a – 1e are true of A and B) then the act by which A threatens B is permissible iff the act by which B threatens A is permissible.

Symmetry is highly plausible given that symmetrical self-defenders such as Smith and Jones are similar in every respect that is relevant for determining the permissibility of their acts. How similar must the defenders be to satisfy Symmetry? Start with an easy case; suppose they are atom-for-atom duplicates, have exactly similar surroundings, and mirror each other’s bodily movements perfectly (although there is still some objective chance of one’s surviving and killing the other).Symmetryseems true of such defenders. I don’t think thatSymmetryplausibly requires perfect natural similarity or even perfect moral similarity. It could apply to two defenders even if one was, for example, more culpable than the other. But I will not try to defend this claim here. Whether it is true has no bearing on Symmetry’s plausibility; it matters only for determining the range of actual and hypothetical cases in whichSymmetryapplies. For the sake of simplicity, I will assume that Smith and Jones are perfectly naturally similar, although there is an objective chance of one’s surviving and killing the other. (Note: this is compatible with the possibility of each dying at the hands of the other.)

If No Deontic Gap is false, then the defenders’ acts are neither permissible nor impermissible. This is hard to believe. Surely, each defender’s act would be either permissible or impermissible if one of them had pulled the trigger on his rifle just before the other pulled the trigger on his. We shouldn’t think that the deontic laws of the universe have collapsed just because each happened to pull the trigger exactly when the other did. There may be interesting reasons for rejecting No Deontic Gap, but I will not consider any in this post. (I’d be interested to hear from anyone who thinks there might be good reason to reject No Deontic Gap.)

The problem is this: If the Standard View is true, then at least one of 1 – 8 must be false. In fact, it seems, the only claims that can reasonably be questioned are 5, 6, and 8. Claims 1 through 4 can just be stipulated, and claim 7 seems undeniable. So if the Standard View is true, then it seems we must reject either 5, 6, or 8. But the conjunction of 5, 6, and 8 seems more plausible than the Standard View. We therefore have good reason to reject the Standard View. I call this the problem of symmetrical threats. First, I will prove that the Standard View is incompatible with the conjunction of 1—8. Next, I will briefly explain why I believe it is difficult to reject 5—No Other Permission. Finally, I will consider one modification of the Standard View that is compatible with 1—8. I will argue that this proposed modification fails to solve the problem. I end on a note of skepticism; currently, I can think of no solution to the problem of symmetrical threats that is more plausible than simply rejecting the Standard View in favor of a view on which the moral status of an act which threatens to kill an attacker is in no way determined by the moral status of the act by which the attacker threatens others.

2. Proof of Incompatibility

Let us first restate the Liability and Defensive Conditions:

Liability Condition: x is liable to be killed for threatening to kill or seriously injure y iff (i) the act by which x threatens y is impermissible and (ii) x meets any subjective criteria that are necessary for x’s being liable to be killed.

Defensive Condition: The act by which x threatens to kill y is permissible iff either (iii) y is liable to defensive killing and x’s act is both necessary and proportionate, or (iv) x has a non-liability based permission to threaten to kill y.

The conjunction of Liability Condition and Defensive Condition is incompatible with the conjunction of claims 1—8.

Proof:

According to No Deontic Gap, Smith’s act is either permissible or impermissible. In either case, we derive a contradiction.

This may be a lot to take in quickly, so here is the intuitive idea: Suppose that Smith’s act is impermissible. Then according to the Standard View, he is liable to be killed. If Smith is liable to be killed, then threatening to kill him (which Jones is doing) is permissible. Thus, Jones’s act is permissible. But if Jones’s act is permissible, then so is Smith’s, for the two men are perfectly symmetrical. And of course, if Smith’s act is permissible, it can’t be impermissible. So Smith’s act isn’t impermissible. Contradiction!

Working backwards, suppose that Smith’s act is permissible. Then so is Jones’s, for the two men are perfectly symmetrical. And of course, if Jones’s act is permissible, it can’t be impermissible. So Jones’s act isn’t impermissible. But then according to the Standard View, Jones isn’t liable to be killed. But Smith cannot be permitted to kill Jones for any reason other than that Jones is liable to be killed. And so Smith’s act isn’t permissible. Contradiction!

3. No Other Permission

I think that for those who wish to preserve the Standard View, the first place to try to push is No Other Permission. But I do not see what kind of permission or justification Smith and Jones could have to threaten to kill anyone, if not one that is grounded in considerations of liability.

Neither has a lesser-evil justification to threaten the other, and so neither is permitted on grounds of lesser evil to do so. It may be useful to compare Symmetry Case 1 with a hypothetical case presented by Jeff McMahan in which each of two symmetrically situated agents apparently has a lesser-evil justification to threaten to kill the other:

… Two Roman prisoners are credibly threatened by the guards at the Colosseum that unless they fight to the death as gladiators, they will both be killed. …There is no difference between them that would give one of them a duty to sacrifice himself for the sake of the other. And it cannot be the case that each is morally required to sacrifice himself for the other, for in that case if both tried to do their duty, neither would kill the other and both would be killed by the guards. … It is better that one should live than that both should die. It seems, therefore, that each has a lesser-evil justification for trying to kill the other.[4]

Each Roman prisoner has a lesser-evil justification for threatening to kill the other only because that decreases the chance of both dying. But in Symmetry Case 1, it is not the case that each defender’s threatening to kill the other decreases the chance of both dying; so in Symmetry Case 1, considerations of lesser-evil do not give either defender a justification or a permission to threaten to kill the other.

What about desert? Might each defender be justified, and hence, permitted, on grounds of desert to kill the other? Note that if each acts permissibly, then by Deontic Monoletheism neither acts impermissibly, and so neither satisfies Liability Condition. Thus, in order to uphold the Standard View by appealing to permissions of desert, we must say that each defender is permitted to threaten to kill the other because the other deserves to be killed, despite the fact that neither is liable to be killed. Call this the desert view.

I have several complaints. First, the view that individuals deserve to be killed is morally repugnant. Second, if neither defender is liable to be killed, then even if he deserves to be killed, it is hard to believe that the other is permitted to kill him. The usual way of understanding liability is in terms of rights forfeiture. According to this understanding, one’s being liable to suffer harm x is defined as one’s having forfeited one’s right not to have x inflicted on him; if one isn’t liable to suffer harm x, then one retains one’s right not to have x inflicted on him. But if each defender retains his right not to be killed, then even if he deserves to be killed, it is hard to see how the other can be permitted to kill him. It is hard to see how considerations of desert can, in this way, override individual rights. Third, on the desert view each defender deserves to be killed even though the act by which he threatens to kill the other is permissible. It is hard to believe that one can deserve to be killed for performing an act that is morally permissible, even if the intention with which one acts is morally reprehensible. Fourth, if a fully culpable aggressor deserves to be killed, and this gives others a desert-based justification to kill him, it would seem to follow that others may kill him even if killing him isn’t necessary for stopping his threat. In other words, the act of killing a culpable aggressor needn’t satisfy the necessity condition in order to be morally justified and permissible. One can have a positive moral reason for killing a culpable aggressor, and hence, can be permitted to kill the aggressor, even if one can simply deflect the aggressor’s threat in a way that results in no harm to anyone. That is very hard to believe.

There are other kinds of permission that we might consider, but ultimately I think it will be hard to reject No Other Permission. A more promising solution to the problem of symmetrical threats may be to reject the Standard View as stated, but accept a slightly modified version of that view. I will now consider one way of doing that.

4. Adding a ‘right intention’ clause to Defensive Condition

One way to emend the Standard View appeals to the relevance of intention to permissibility. There may be cases in which, although one has a justification for acting a certain way, one acts impermissibly in virtue of possessing a wrongful intention. For example, consider

Perhaps, although there is a lesser-evil justification for turning the trolley, the driver acts impermissibly because she acts with a wrongful intention—she intends to kill the one. Similarly, one might argue that although Smith and Jones are liable to defensive killing, and so there is a liability-based justification for threatening to kill either of them, each acts impermissibly because he acts with a wrongful intention. We can replace Defensive Condition with

Revised Defensive Condition: If x threatens to kill y and x doesn’t have a non-liability-based permission to threaten to kill y, then the act by which x threatens to kill y is permissible iff (iii) y is liable to defensive killing, (iv) x’s act is both necessary and proportionate, and (v) x acts without a wrongful intention.

The inconsistency with 1—8 is resolved by adding a ‘right intention’ clause to Defensive Condition. Because neither Smith nor Jones satisfies the ‘right intention’ clause, neither satisfies Revised Defensive Condition. Although each has a liability-based justification for threatening to kill the other, this isn’t sufficient to make his act permissible. Both are liable to defensive killing, yet both act impermissibly.[5] The conjunction of Liability Condition and Revised Defensive Condition is compatible with claims 1 – 8. Looking at the proof of incompatibility, we see that the inference from P2 to P3 in the first reductio is blocked. We can no longer infer ‘Jones’s act is permissible’ from ‘Smith is liable to be killed’.

However the proposal is unsuccessful, for consider

Symmetry Case 2. Like Symmetry Case 1, but with the following backstory: Each defender falsely believes that the other defender is maliciously trying to kill him, and each attacks the other without malice, intending only to defend his own life. However, each knows that his belief about the other’s intentions could easily be mistaken, and that the other may very well be innocent. Moreover each knowingly and culpably ignores crucial evidence that bears on the question of the other’s innocence, for neither cares about harming the innocent. If either had paid attention to the evidence, he would have realized that the other had no prior intention of attacking him, and the conflict would have been avoided.

I claim that in Symmetry Case 2, Smith and Jones meet the subjective criteria for liability to be killed. In particular, each acts recklessly and is culpable for his recklessness. Denying that each meets the subjective criteria sets the bar for liability unreasonably high. However, because neither defender acts with a wrongful intention, each satisfies the ‘right intention’ clause. Hence, the inference from P2 to P3 in the first reductio is valid.

5. Conclusion

Perhaps the most plausible solution to the problem of symmetrical threats is to simply reject the Standard View in favor of a view of the ethics of defensive killing on which the moral status of an act of defensive killing isn’t explained in terms of the moral status of the act by which the person to be killed threatens others. For it is the Standard View’s requirement of moral asymmetry between agents who threaten each other that is problematic, insofar as there are cases that seem to involve no such asymmetry. But views that do not require this kind of asymmetry seem implausible, even if they avoid the problem of symmetrical threats. Pacifism presents an easy solution to the problem of symmetrical threats: Even if an attacker’s threat is impermissible, this doesn’t make it permissible to threaten to kill him, since it is never permissible to kill a person. Thus, in Symmetry Cases 1 and 2, both Smith and Jones act impermissibly. But pacifism seems too conservative. On this view, even the most malicious and dangerous villains may not be killed.

Hobbesian realism also presents a simple solution to the problem of symmetrical threats. If an attacker threatens to kill one, this is enough to permit one to kill the attacker. Thus, both Smith and Jones act permissibly. But realism seems too permissive. If the act by which an attacker threatens to kill one is morally justified, it is hard to see how one could be permitted to kill the attacker, especially if one is acting in a way that would render one liable to be killed according to less permissive views, such as the Standard View.

Certain types of consequentialism would also avoid the problem of symmetrical threats. But consequentialism is infamous for seeming both too permissive and too conservative. Depending on what is at stake, one who is innocent may be required to allow even the most malicious villain to kill one. (For example, if the villain’s remaining life would contain slightly more good than the innocent person’s life.) Alternatively, one may be permitted (and required) to kill those who are innocent in order to promote the greater good, even to a degree that seems trivial.

Is there a more plausible approach that avoids the problem of symmetrical threats?

[3] An actual case of this kind occurred during the Vietnam war, in which an American marine, Carlos Hathcock, shot and killed a Vietnamese sniper known as “the cobra” through the scope of the latter’s own rifle. (Charles Henderson, Marine Sniper: 93 Confirmed Kills (Berkeley Books, 2001)).

2 responses to “The Problem of Symmetrical Threats”

Hi Tim, cool paper! It seems to me that both agents in the symmetry case forfeit their right to life, and hence each acts permissibly in killing the other. This suggests that it’s the Liability Condition, not the Defensive Condition, that needs to be revised. In particular, I think, we should want to revise clause (i) of the Liability Condition to refer not only to impermissible threats but also to (something like) the disposition to issue said threat even if it were to be impermissible.

This then yields:

Revised Liability Condition: x is liable to be killed for threatening to kill or seriously injure y iff (i) the act by which x threatens y is either impermissible, or, if permissible, x was disposed to issue the threat even had it been impermissible, and (ii) x meets any subjective criteria that are necessary for x’s being liable to be killed.

Hi Richard!
Thanks! I like your idea. I have two thoughts about it.
First, it seems to me that even if we accept your proposal (and there may be good reason to accept it) the problem would persist because there are possible cases of symmetrical self-defense in which each defender is culpable for actively threatening to kill the other but neither is disposed to threaten the other if the other isn’t threatening him. Let’s imagine a case in which neither defender considers it good sport to kill the other while the other isn’t trying, or isn’t disposed to try, to kill him; as a result, neither is disposed to threaten a non-threatening person. Suppose we say that in this case each defender acts permissibly in attacking the other because the other is liable to be killed. We can then ask why each is liable to be killed. I don’t think we can appeal to the answer that you suggest. Suppose that with respect to each defender, enough of the nearby possible worlds in which it would be impermissible for him to threaten to kill the other defender are worlds in which he doesn’t issue any threat (for the reasons mentioned above). Then, it seems, the case we are imagining is one in which neither defender has the disposition that you mention. (Correct me if I’ve got it wrong.)

Second, your proposal makes me think that I shouldn’t have framed the puzzle specifically in terms of the morality of acts. It seems to me that being disposed to act in a threatening manner is sometimes sufficient for posing a threat, and that therefore culpability for a disposition to threaten others might be sufficient for liability, at least in certain cases. Therefore, because the Standard View links liability with permissibility, it seems I should be talking about the permissibility of threats rather than the permissibility of acts. If we do this, we should say that each defender loses his right not to be killed even before pulling the trigger; and that seems very plausible. It also makes me wonder how disposed each defender has to be in order to be liable.